As a teenager playing for his hometown Brynas IF Gavle, Nicklas Backstrom was highly touted as "the next Peter Forsberg," and apparently with good reason. Like Forsberg, Backstrom has great vision and passing and is devilishly tough to knock off the puck.
Forsberg, however, in his heyday, was the best player in the world. In 2002-2003 Forsberg won the Art Ross Trophy as the NHL's points leader with 29 goals, 76 assists, and 106 points, a performance which earned him the Hart Trophy as league MVP as well. Furthermore, Forsberg only played 19:20 a night that season. If Backstrom's hadn't played so little early on in his NHL career, he might have exceeded that total in his rookie season, as well as his second and third seasons.
Unfortunately, we don't have Corsi and other advanced statistics from Forsberg's young days, so I'll have to do a comparison of basic stats via Hockey-Reference.
Hockey-Reference, on each player page, puts up a table called "adjusted," which is helpful to compare players across eras, normalizing schedules (but not necessarily games played) to 82 games, roster sizes to 18 skaters, goals per game to six, and assists per goal to 1.67. In other words, they've already done a lot of the work we'd otherwise have had to do by hand. (More information here)
So, how does Backstrom look compared to Forsberg in terms of Hockey-Reference's adjustment?
(It's worth noting that on average young players really start becoming successful around age 20, and during those young years experience rapid development, according to Copper and Blue)
(All stats adjusted)
At first glance it looks like Backstrom and Forsberg are almost equals. While Forsberg's rookie season was much better than Backstrom's, in terms of season-by-age, their 21 and 22-year old seasons are almost identical. Backstrom seems to be slightly better goal scorer, and Forsberg a slightly better playmaker.
The adjustments, however, do not take team into account. In 1994-1995, the shortened season, 21-year old Forsberg's Nordiques returned to first in their division for the first time since 1986. They were first in goals for and 9th in goals against. And Forsberg was stuck at second on the depth chart at center behind Joe Sakic. Even though he was a second liner that year, his linemates--some combination of Owen Nolan, Scott Young, Valeri Kamensky, and Wendel Clark, I guess--were pretty good: Kamensky's 30 points adjust to between 55 and 60 points. When you consider the circumstances of Backstrom though--playing with the league's best player in Alex Ovechkin, and Viktor Kozlov in his 21-year old season--Forsberg did much more with less. Both teams were loaded, but Forsberg played with lesser players, and probably in a tougher conference as well, not to mention less TOI.
In Forsberg's second season, a similar storyline took hold. The Avalanche had a deadly offense, a top-ten defense, and once again Forsberg, from the second line, had a terrific season. While Backstrom had a great season as well in 2009-2010, it came with the weakest schedule in the league, while at least the Avalanche were middle of the pack. Another big difference? Forsberg's Avalanche won the Stanley Cup.
The following season Forsberg started having better statistical seasons than Sakic, though I don't think he supplanted Sakic as the #1 center (I think Sakic assumed more defensive responsibilities, since he became a minus player, though I can't remember for sure).
To answer the original question: yes, Backstrom is still like Forsberg. They score at similar rates, in terms of goals, assists, and points too. Forsberg was simply a more dominant player and could do more with less (though presumably against weaker competition, though on the other hand in the no-cap era teams could load up on defense more than they can now).
That doesn't mean Backstrom cannot get that good too--maybe it's just that he has never had to. Honestly, Sakic-Forsberg strikes me as a bit similar to Crosby-Malkin. While Backstrom hasn't shown an ability to be as dominant as Forsberg/Malkin, he's more durable and may be better in the long run.